The finite-time isothermal process is fundamental in quantum thermodynamics yet complicated with combination of changing control parameters and the interaction with the thermal bath. Such complexity prevents the direct application of the traditional thermodynamics measurement of the relevant quantities. In this paper, we provide a discrete-step method to separate the work done and the heat exchange in the isothermal process by decomposing the process into piecewise adiabatic and isochoric processes. The piecewise control scheme makes it possible to simulate the whole process on a generic quantum computer, which provides a new platform to experimentally study quantum thermodynamics. We implement the simulation on ibmqx2 to show the $\mathrm{\mathcal{C}/τ}$ scaling of the extra work in the finite-time isothermal process.
We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
Studying out-of-equilibrium physics in quantum systems under quantum quench is of vast experimental and theoretical interests. Using periodic quantum quenches, we present an experimentally accessible scheme to simulate the quantum Zeno and anti-Zeno effects in an open quantum system of a single superconducting qubit interacting with an array of transmission line resonators. The scheme is based on the following two observations: Firstly, compared with conventional systems, the short-time non-exponential decay in our superconducting circuit system is readily observed; and secondly, a quench-off …
Superconducting quantum circuits is one of the leading candidates for a universal quantum computer. Designing novel qubit and multiqubit superconducting circuits requires the ability to simulate and analyze the properties of a general circuit. In particular, going outside the transmon approach, we cannot make assumptions on anharmonicity, thus precluding blackbox quantization approaches and necessitating the formal circuit quantization approach. We consider and solve two issues involved in simulating general superconducting circuits. One of the issues is the handling of free modes in the circu…
Simulation of materials by using quantum processors is envisioned to be a major direction of development in quantum information science. Here we exploit the mathematical analogies between a triangular spin lattice with Dzyaloshinskii-Moriya coupling on one edge and a three-level system driven by three fields in a loop configuation to emulate spin-transport effects. We show that the spin transport efficiency, seen in the three-level system as population transfer, is enhanced when the conditions for superadiabaticity are satisfied. We demonstrate experimentally that phenomena characteristic to s…
We theoretically investigate the simulation of moving cavities in a superconducting circuit setup. In particular, we consider a recently proposed experimental scenario where the phase of the cavity field is used as a moving clock. By computing the error made when simulating the cavity trajectory with SQUIDs, we identify parameter regimes where the correspondence holds, and where time dilation, as well as corrections due to clock size and particle creation coefficients, are observable. These findings may serve as a guideline when performing experiments on simulation of moving cavities in superc…
Quantum walk (QW) in presence of lattice disorders leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a scheme to realize the discrete time QW by placing a pair of superconducting qubits on each site of a 1D lattice and treat…
We propose possible approaches for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. The standard Jaynes-Cummings-Hubbard setup considered in several recent studies can readily be used as a quantum simulator for a number of relevant phenomena, including the interaction with external magnetic fields and spin-orbit coupling. A more complex setup where multiple qubits and multiple resonator modes are utilized in the simulation gives a higher level of complexity, including the simulation of particles with high spin values and allowing more dire…
We present a novel method for solving eigenvalue problems on a quantum computer based on spectroscopy. The method works by coupling a "probe" qubit to a set of system simulation qubits and then time evolving both the probe and the system under Hamiltonian dynamics. In this way, we simulate spectroscopy on a quantum computer. We test our method on the IBM quantum hardware for a simple single spin model and an interacting Kitaev chain model. For the Kitaev chain, we trace out the pseudo-topological phase boundary for a two-site model.
We propose an experimental scheme to simulate the dynamical quantum Hall effect and the related interaction-induced topological transition with a superconducting-qubit array. We show that a one-dimensional Heisenberg model with tunable parameters can be realized in an array of superconducting qubits. The quantized plateaus, which is a feature of the dynamical quantum Hall effect, will emerge in the Berry curvature of the superconducting qubits as a function of the coupling strength between nearest neighbor qubits. We numerically calculate the Berry curvatures of two-, four- and six-qubit array…
Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than one hundred, their applicability remains plagued by the presence of noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system s…
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the `shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting …
Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experi…
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to simulate quantum lattice models with long-range hopping. Our approach is based on an exact mapping between periodically driven quantum systems and one-dimensional lattices in the synthetic Floquet direction. By engineering a periodic drive with a power-law spectrum, we simulate a lattice with long-range hopping, whose decay exponent is freely tunable. We propo…
We describe an efficient and scalable framework for modeling crosstalk effects on quantum information processors. By applying optimal control techniques, we show how to tuneup arbitrary high-fidelity parallel operations on systems with substantial local and nonlocal crosstalk. Simulations show drastically lower error rates for a 2D square array of 100 superconducting transmon qubits. These results suggest that rather than striving to engineer away undesirable interactions during fabrication, we can largely mitigate their effects through careful characterization and control optimization.
We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long distance entanglement (LDE), namely a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with XX nearest-neighbor interactions. In both cases we discuss a suitable protocol for the adiabatic preparation of the ground…
$\textbf{scqubits}$ is an open-source Python package for simulating and analyzing superconducting circuits. It provides convenient routines to obtain energy spectra of common superconducting qubits, such as the transmon, fluxonium, flux, cos(2$ϕ$) and the 0-$π$ qubit. $\textbf{scqubits}$ also features a number of options for visualizing the computed spectral data, including plots of energy levels as a function of external parameters, display of matrix elements of various operators as well as means to easily plot qubit wavefunctions. Many of these tools are not limited to single qubits, but ext…
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with …
Understanding complex quantum matter presents a central challenge in condensed matter physics. The difficulty lies in the exponential scaling of the Hilbert space with the system size, making solutions intractable for both analytical and conventional numerical methods. As originally envisioned by Richard Feynman, this class of problems can be tackled using controllable quantum simulators. Despite many efforts, building an quantum emulator capable of solving generic quantum problems remains an outstanding challenge, as this involves controlling a large number of quantum elements. Here, employin…
We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct non-equilibrium second order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we…
Multiple bosons undergoing coherent evolution in a coupled network of sites constitute a so-called quantum walk system. The simplest example of such a two-particle interference is the celebrated Hong-Ou-Mandel interference. When scaling to larger boson numbers, simulating the exact distribution of bosons has been shown, under reasonable assumptions, to be exponentially hard. We analyze the feasibility and expected performance of a globally connected superconducting resonator based quantum walk system, using the known characteristics of state-of-the-art components. We simulate the sensitivity o…
We propose a scheme for simulating 3+1, 2+1, 1+1 Dirac equation for a free spin-1/2 particle with superconducting josephson circuits consisting of five qubits, four qubits, two qubits respectively. In 3+1D and 2+1D, the flux qubit1 driven by a resonant pulse is in the superposition state of its own two eigenstatesis, and it is used as a bus to induce the (blue)red-sideband excitation consisting of a magnetic pulse acting resonantly on two levels of the flux qubit2 and the energy levels of one phase qubit, which yields two (Anti)Jaynes-Cummings interactions with one driving pulse and reduces th…
We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon-electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn-Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular e…
Simulating complex molecules and materials is an anticipated application of quantum devices. With strong quantum advantage demonstrated in artificial tasks, we examine how such advantage translates into modeling physical problems of correlated electronic structure. We simulate static and dynamical electronic structure on a superconducting quantum processor derived from Google's Sycamore architecture for two representative correlated electron problems: the nitrogenase iron-sulfur molecular clusters, and $α$-ruthenium trichloride, a proximate spin-liquid material. To do so, we simplify the elect…
Spectroscopy is a crucial laboratory technique for understanding quantum systems through their interactions with electromagnetic radiation. Particularly, spectroscopy is capable of revealing the physical structure of molecules, leading to the development of the maser - the forerunner of the laser. However, real-world applications of molecular spectroscopy are mostly confined to equilibrium states, due to computational and technological constraints; a potential breakthrough can be achieved by utilizing the emerging technology of quantum simulation. Here we experimentally demonstrate that a supe…
Simulating Electron Transfer on Noisy Quantum Computers
Institute of Engineering Thermodynamics, German Aerospace Center (DLR)（德国航空航天中心工程热力学研究所）；Helmholtz Institute Ulm（乌尔姆亥姆霍兹研究所）；Institute of Software Technology, German Aerospace Center (DLR)（德国航空航天中心软件技术研究所）；HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；Department of Physics, Ulm University（乌尔姆大学物理系）
Quantum systems are notoriously difficult to simulate with classical means. Recently, the idea of using another quantum system - which is experimentally more controllable - as a simulator for the original problem has gained significant momentum. Amongst the experimental platforms studied as quantum simulators, superconducting qubits are one of the most promising, due to relative straightforward scalability, easy design, and integration with standard electronics. Here I review the recent state-of-the art in the field and the prospects for simulating systems ranging from relativistic quantum fie…
We investigate the Cherenkov radiation triggered by qubit acceleration simulated by superconducting circuit. By analyzing the radiation probability, we confirm the existence of Cherenkov speed threshold, implying that simulating superluminal qubit motion is possible for such a scenario. A question immediately arises: Is such motion compatible with the causality principle? To address the question, we perform a causality test on the simulating system based on the recently developed notion of temporal quantum correlations, pseudo-density matrix and temporal quantum steering. The results suggest t…
Circuit QED on a chip has become a powerful platform for simulating complex many-body physics. In this report, we realize a Dicke-Ising model with an antiferromagnetic nearest-neighbor spin-spin interaction in circuit QED with a superconducting qubit array. We show that this system exhibits a competition between the collective spin-photon interaction and the antiferromagnetic nearest-neighbor spin-spin interaction, and then predict four quantum phases, including: a paramagnetic normal phase, an antiferromagnetic normal phase, a paramagnetic superradiant phase, and an antiferromagnetic superrad…
We introduce a toolbox for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We consider as well possible setups for simulating the superluminal motion of a mirror, finding a link with the superradiant phase transition of the Dicke model.
The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms on near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable tensor n…
Quantum simulation is a potentially powerful application of quantum computing, holding the promise to be able to emulate interesting quantum systems beyond the reach of classical computing methods. Despite such promising applications, and the increase in active research, there is little introductory literature or demonstrations of the topic at a graduate or undergraduate student level. This artificially raises the barrier to entry into the field which already has a limited workforce, both in academia and industry. Here we present an introduction to simulating quantum systems, starting with a c…
Simulating the Dynamics of Markovian Quantum Processes by Quantum Collision Models on Quantum Computers
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Q-CTRL；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute（理化学研究所先导研究本部）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
We propose a quantum algorithm for simulating spin models based on periodic modulation of transmon qubits. Using Floquet theory we derive an effective time-averaged Hamiltonian, which is of the general XYZ class, different from the isotropic XY Hamiltonian typically realised by the physical setup. As an example, we provide a simple recipe to construct a transverse Ising Hamiltonian in the Floquet basis. For a 1D system we demonstrate numerically the dynamical simulation of the transverse Ising Hamiltonian and quantum annealing to its ground state. We benchmark the Floquet approach with a digit…
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization that only addresses noninteracting particles in the presence of disorder, greatly challenges this concept because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, an…
Observing Quantum Correlation Dynamics in Tunable Superconducting Bose-Hubbard Simulators
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [Nature Photonics $\textbf{9}$…
Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark phy…
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe tha…
